Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol

LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish

Xinqian LENG (1), Hubert CHANSON (1) (*), Matthews GORDOS (2) and Marcus RICHES (2)

(1) The University of Queensland, School of Civil Engineering, Brisbane QLD 4072, Australia

(2) New South Wales Department of Primary Industries, 1243 Bruxner Highway, Wollongbar NSW 2477,

Australia

(*) Corresponding author, Ph.: (61 7) 3365 3619, Fax: (61 7) 3365 4599, Url:

http://www.uq.edu.au/~e2hchans/, Email: [email protected]

Declarations of interest: none.

ORCID numbers:

Xinqian LENG: 0000-0001-8472-7925

Hubert CHANSON: 0000-0002-2016-9650

Abstract

Low-level river crossings can have negative impacts on freshwater ecosystems, including blocking upstream fish passage. In order to restore upstream fish passage in culverts, we developed physically-based design methods to yield cost-effective culvert structures in order to maintain or restore waterway connectivity for a range of small-bodied fish species. New guidelines are proposed for fish-friendly multi-cell box culvert designs based upon two basic concepts: (1) the culvert design is optimised for fish passage for small to medium water discharges, and for flood capacity for larger discharges, and (2) low-velocity zones in the culvert barrel are defined in terms of a percentage of the wetted flow area where the local longitudinal velocity component is less than a characteristic fish speed linked to swimming performances of targeted fish species. This approach is novel and relies upon an accurate physically-based knowledge of the entire velocity field in the barrel, specifically the longitudinal velocity map, because fish tend to target low-velocity zone

1 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

(LVZ) boundaries. The influence of the relative discharge threshold Q1/Qdes, characteristic fish swimming speed Ufish, and percentage of flow area on the size of box culvert structures was assessed. The results showed that the increase in culvert size and cost might become significant for a smooth culvert barrel with

Ufish < 0.3 m/s and Q1/Qdes > 0.3, when providing 15% flow area with 0 < Vx < Ufish. Similar trends were seen for culvert barrel with recessed cell(s).

Keywords: Box culverts; Upstream fish passage; Design guidelines; Low velocity zones.

1. INTRODUCTION

Low-level river crossings, i.e. culverts and causeways, are important for delivering a range of valuable socio- economic services, including transportation and flood control. However, such structures are also known to have negative impacts on freshwater river system morphology and ecology, including the blockage of upstream fish passage (WARREN and PARDEW 1998, ANDERSON et al. 2012). The manner in which waterway crossings block migrating fish include perched outlets and excessive vertical drops at the culvert exit, high velocity and insufficient water depth in the culvert barrel, debris accumulation at the culvert inlet, and standing waves in the outlet or inlet (BEHLKE et al. 1991, OLSEN and TULLIS 2013). In particular for smaller, weaker-swimming fish, the upstream traversability of the culvert barrel can be a major obstacle, particularly at high water velocities. In order to restore upstream fish passage in culverts over the widest extent possible, the aim of this work is to use physically-based design methods to yield cost-effective culvert structures in order to maintain and restore waterway connectivity for a range of small-bodied fish species.

Freshwater fish species constitute about one quarter of all living vertebrates, and are considered an at-risk group due to deleterious habitat impacts. In Australia, for example, there are about 250 freshwater fish species, with approximately 30 % listed as threatened under State and Commonwealth legislation (ALLEN et al. 2002, LINTERMANS 2013). The negative effects of river crossings on freshwater fish species are well documented in the literature (WARREN and PARDEW 1998, BRIGGS and GALAROWICZ 2013). Culvert structures often create physical or hydrodynamic barriers that prevent or reduce access to essential breeding or feeding habitats. The direct consequences of losing access too and fragmentation of river habitats on fish

2 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

encompass reduced recruitment, restricted range size, and changes in fish population composition, all of which being potentially exacerbated by long-term climate changes (DYNESIUS and NILSSON 1994,

O'HANLEY 2011, WILKES et al. 2018). Apart from impeding fish passage, road crossing barriers can act in other disruptive ways. Examples include: suspended and bed load sediment transport, river substrate composition and morphology changes, and nutrients and large woody debris supply (HOTCHKISS and FREI

2007). The resulting environmental changes can extend across river reaches in both the downstream and upstream directions, creating conditions potentially favourable to the establishment and development of non- native invasive species (OLSON and ROY 2002, MILT et al. 2018). The end result can often be a reorganisation of the riverine biophysical structure, most often associated with a reduction in the numbers and diversity of native fish species (O'HANLEY 2011).

Given the enormous environmental problems created by road crossings, it is not surprising that various culvert design guidelines (e.g. FAIRFULL and WITHERIDGE 2003, HUNT et al. 2012) have been developed to facilitate upstream fish passage in culverts (refer to Table 1), albeit not always successfully.

Recent field and laboratory work has yielded markedly different recommendations (Table 2). Relatively little work has been published regarding the development of systematic design methods for cost-efficient fish- friendly culverts, to deliver un-impeded fish connectivity over wide geographic areas. In most cases, design methods have focused predominantly on baffle installation and boundary roughening along the culvert barrel invert to slow down the water velocity, although the additional flow resistance can reduce drastically the culvert discharge capacity for a given afflux. The afflux is the increase in upstream water level caused by the presence of the culvert, typically derived from design charts or hydraulic modelling (HERR and BOSSY

1965, CHANSON 1999,2004). Such a reduction in culvert capacity markedly increases the total cost of the culvert for a design discharge and afflux, as demonstrated by LARINIER (2002) and OLSEN and TULLIS

(2013). In only a few cases have more robust engineering-based methods been examined. This includes works by PAPANICOLAOU and TALEBBEYDOKHTI (2002), HOTCHKISS and FREY (2007), and

OLSEN and TULLIS (2013).

In this article, a hydraulic engineering approach is used to rationally devise fish-friendly standard box culverts, which are the preferred culvert design for effective fish passage relative to pipe culverts (BRIGGS and GALAROWICZ 2013). Structurally, this new design method is most closely related to aero- and hydro-

3 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

dynamic studies, in that it does not assume a simplistic one-dimensional flow motion. Rather, culvert barrel flows are considered as a complex three-dimensional flow, in which turbulence is generated by both bed and sidewall boundary friction. The main focus is on improving upstream fish passage in the box culvert barrel to restore connectivity within the riverine system as a whole. The proposed method is more general in comparison to previous approaches. The benefits of this are twofold. First, the design method is especially well suited to meet the life-cycle requirements of small-bodied native fish species which regularly change habitats and migrate for recruitment and habitat viability requirements in different parts of a river system.

Second, in an effort to keep the design process as simple as possible, and keep cost to a minimal, the design method presented in this article can be applied in a straight-forward manner to any watershed. The methods and results below are largely based on CHANSON and LENG (2018).

1.1. Current practices in hydraulic engineering design of culverts

The primary constraints in the design of a culvert (Fig. 1) are minimising: (a) costs, and (b) afflux. The design procedure is traditionally divided into two parts. First the design rainfall and runoff event is selected based upon the culvert purposes, design data, and site constraints; thereby yielding an estimate of the design discharge Qdes. A maximum acceptable afflux hmax, at design flow conditions, is then set by the asset owner based upon an impact assessment of the culvert structure on the upstream catchment and embankment.

Second the culvert barrel size is selected by an iterative procedure and the optimum size is the smallest barrel size allowing for inlet control operation (HERR and BOSSY 1965, HEE 1969, CHANSON 2000,2004). The resulting optimum design is to operate as an open channel system at the design discharge, with critical flow conditions typically occurring in the barrel in order to maximise the discharge per unit width and to reduce the barrel cross-section area. Altogether, the hydraulic design is basically an optimum compromise between discharge capacity, afflux and construction costs.

Current hydraulic engineering design guidelines of box culverts do not encompass less-than-design flow conditions (Q < Qdes). Yet fish passage can occur as soon as the water discharge is non-zero: Q > 0. As such, new design guidelines for fish-friendly box culverts are critically needed. A further challenge for the design of fish-friendly culverts is matching swimming performance data to hydrodynamic measurements. Many

4 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

swim tests lack standardised test methods, i.e. two different studies rarely use the same protocol, and the output is either a single-point measurement or a bulk velocity (KATOPODIS and GERVAIS 2016).

2. MATERIALS AND METHODS

Novel engineering design guidelines are considered, based upon two basic concepts:

(a) The culvert design is optimised for fish passage for water discharges Q < Q1; and it is optimised in terms of flood capacity for Q1 < Q < Qdes, with Q1 an upper threshold discharge for less-than-design flow with Q1 <

Qdes.

(b) Since small-bodied fish predominantly swim next to the channel corners and sidewalls (GARDNER

2006, BLANK 2008, JENSEN 2014), in particular small-bodied Australian native fish species (WANG et al.

2016a, CABONCE et al. 2017,2019, GOODRICH et al. 2018), the swimming performance data are related to a fraction (i.e. percentage) of the wetted flow area where:

0Vxfish U (1)

with Vx the local time-averaged longitudinal velocity component and Ufish a characteristic swimming speed of targeted fish species, set by a regulatory agency or based upon biological observations and endurance swimming test data.

A novel approach is the provision of a minimum relative flow area where the longitudinal water velocity is less than a characteristic fish swimming speed (Eq. (1)). The proposed design method aims to be sound, simple, economically acceptable and meet engineering standards. Three practical questions are tested herein with respect to influencing the size and cost of standard box culverts: (1) what is the effect of the relative threshold Q1/Qdes, (2) what is the influence of the percentage of low velocity area, and (3) what is the impact of the characteristic fish swimming speed Ufish?

A sensitivity analysis was conducted for two multi-cell box culvert structures, typical of two-lane roadway projects in eastern Australia (Table 3). Natural tailwater conditions were used: i.e., gauge data (Culvert 1,

Fig. 2) and uniform equilibrium flow conditions (Culvert 2). The culvert barrel size was calculated to achieve the smallest barrel size with inlet control for the design flow rate Qdes and maximum acceptable

5 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

afflux hmax, with the culvert barrel invert at natural ground level, in line with current hydraulic engineering design guidelines (HERR and BOSSY 1965, HEE 1969, CHANSON 2004). The basic design calculation output was the number of cells (Ncell)des, listed in Table 3.

For less-than-design flow conditions, hydraulic engineering calculations were based upon complete calculations and numerical modelling validated with detailed physical data. In addition and for Culvert 1, detailed three-dimensional computational fluid dynamics (3D CFD) calculations were undertaken. The focus of the latter calculations was to test a lower invert, allowing to retain a 0.3 m deep pool of water in the culvert barrel during dry to very-low flow conditions.

The hydraulic engineering calculations were undertaken for a range of less-than-design discharges: 0.1 <

Q/Qdes < 0.5. The tailwater conditions were subcritical and the culvert flow remained subcritical with outlet control. The targeted fish species were originally small-body Australian native species, including Empire

Gudgeon, Firetail Gudgeon, Western Carp Gudgeon Striped Gudeon, Mountain Galaxias, Southern Pygmy

Perch, Unspecked Hardyhead, Common Jollytail, Olive Perchlet, Fly-specked Hardyhead, Australian Smelt,

Duboulay’s Rainbowfish, as well as juvenile Australian Bass, Macquarie Perch, Murray Cod, River

Blackfish, Golden Perch, Eel-tailed Catfish, Silver Perch and Spangled Perch. The fish swimming speed of the small-body Australian native fish is typically between 0.3 m/s and 0.6 m/s (HURST et al. 2007,

KAPITZKE 2010, KOEHN and CROOK 2013). Within the current study, we expanded the range of characteristic swimming speeds from 0.2 m/s to 1 m/s to broaden the scope of the study. Fractions of flow area corresponding to low-velocity zones, i.e. fulfilling Equation (1), were tested between 10% and 20%, in line with recent hydrodynamic data (WANG et al. 2018, CABONCE et al. 2019, ZHANG and CHANSON

2018).

The design optimisation is considered in relation to a discharge threshold Q1, rather than flood event duration. The selection is consistent with current engineering practices since the discharge is a design parameter. Note that the selection of a very-low design discharge could result in a smaller, cheaper culvert structure; with potentially poor ecological outcomes in terms of biological considerations. The timing of fish passage must be considered as part of the determination of appropriate hydrology and hydraulic engineering design specifications for culvert structures (HOTCHKISS and FREY 2007, SCHALL et al. 2012). Fish presence may vary between catchments, and fish migration timing might show great disparity with respect to

6 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

stream flows and species. Fish movement in a catchment may be triggered by time of year, runoff events and a number or combination of environmental factors. In Australia, for example, flows are one of the main triggers for fish to initiate migrations, with increasing / high flows being a significant trigger response

(MALLEN-COOPER 1996, ALLEN et al. 2002).

3. RESULTS

3.1 Basic results

The hydrodynamic calculations resulted in the number of identical culvert barrel cells Ncell required to achieve a given low-velocity zone target, i.e. a percentage of flow area, where 0 < Vx < Ufish for a given less- than-design discharge Q, with Q/Qdes < 1. Typical results are reported in Figures 3 and 4, based the entire design process calculations. Figure 3 shows the increase in number of culvert barrel cells to achieve the low- velocity zone target, i.e. 15% of flow area where 0 < Vx < Ufish, and Figure 4 presents the increase in number of culvert barrel cells to achieve different low-velocity zone targets. For each graph, the vertical axis is the characteristic swimming speed Ufish of the targeted fish species and the lower horizontal axis is the dimensionless number of cells Ncell/(Ncell)des, where Ncell is the number of barrel cells for the fish-friendly culvert design and (Ncell)des is the number of barrel cells for optimum flood capacity design (Table 3). The upper horizontal axis is the relative increase in number of barrel cells compared to the optimum flood capacity design. As a first approximation, the result would correspond to the increase in culvert construction costs to achieve fish passage, in the form of additional precast cell units, although, depending upon the site, the final design might require construction of a second structure or selection of a bridge structure instead of a culvert, all at a much greater cost. That is, the results deliver a lower-bound estimate of the increase in culvert construction costs, and would be, in many cases, an under-estimation.

Overall the results demonstrated conclusively that the cost of a fish-friendly box culvert increases with decreasing characteristic fish swimming speed Ufish, for a given discharge threshold Q1/Qdes and relative size of low velocity zone (%flow area). Similarly, the culvert cost increases with increasing discharge threshold, for a given characteristic fish swimming speed and relative size of low velocity zone; and the cost increases

7 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

with increasing relative size of low velocity zone (%flow area) for a given characteristic fish swimming speed Ufish, and discharge threshold Q1/Qdes. The result may be summarised as:

 Ufish   Culvert Cost  Q/1des Q (2)  %flow area 

The calculations showed a critical impact of the characteristic swimming speed Ufish of targeted fish species.

Culvert cost-sensitivity increases markedly in order to pass small-bodied fish (< 100 mm), and juveniles of large-bodied fish, at swimming speeds less than 0.3 m/s, within the range of investigated flow and boundary conditions. Conversely, a targeted fish speed Ufish > 0.7 m/s would be achievable for Q < 0.5Qdes, but biological implications are that most small-bodied fish would be blocked at these high water velocities. We determined that a key design parameter is the discharge threshold Q1/Qdes. The provision of fish passage capability for Q > 0.5Qdes would be cost prohibitive for small-bodied fish. The selection of 10% < Q1/Qdes <

30% is achievable with more moderate increases in culvert number (Fig. 3), while the selection of Q1/Qdes <

10% does not increase much the culvert number above that required for Qdes flows for Ufish > 0.2 m/s.

The relative size of the low-velocity zone also impacts on the structure costs. Based upon detailed physical modelling for flow boundary conditions with which fish endurance was tested (WANG et al. 2016b,

CABONCE et al. 2019), 15% of flow area with 0 < Vx < Ufish may be an appropriate target (Fig. 4). An important criteria in selecting the low-velocity zone is determining its width / depth to ensure that the zone can easily encompass the size of the target fish species.

3.2 Recessed culvert barrel results

Detailed CFD calculations were conducted for a culvert barrel invert installed 0.3 m below the natural ground level (Fig. 5A). The recessed culvert barrel invert configuration was selected based upon current

NSW guideline recommendations that require a minimum of 0.3 m to pool through the culverts at initiate-to- flow to ensure adequate depth for fish to swim through the culverts (DPI-Fisheries, 2013). First, the results showed a significantly more complicated flow field, compared to a culvert barrel invert at natural ground level (Fig. 5B). For such flow conditions, 22% of the pooled culvert flow area experienced a longitudinal velocity Vx such that 0 < Vx < 0.3 m/s. Second, the calculations demonstrated the same trends as for a culvert

8 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

barrel invert at natural ground level, i.e. Equation (2). Namely, the cost of fish-friendly box culvert increases with decreasing characteristic fish swimming speed Ufish, increasing discharge threshold Q1/Qdes, and increasing percentage of low-flow area.

In summary, the design of a culvert with a recessed "wet" cell, also called a low flow channel, may provide an alternative for low-velocity zones with minimum water depth. However, this option requires more advanced fluid dynamic calculations and likely is more expensive to build compared with standard box culverts with barrel inverts set at natural ground level.

4. DISCUSSION

4.1 Application

The present design approach builds up as a development of current hydraulic engineering design methods

(Concrete Pipe Association of Australasia 1991,2012, CHANSON 1999, QUDM 2013). First the minimum number of cells (Ncell)des is calculated to achieve inlet control at design flow conditions, based upon current standards for optimum flood capacity design at the culvert site. Considerations for upstream fish passage are next embedded into the design methodology, using biological considerations. For the selected discharge threshold Q1, characteristic swimming speed of targeted fish species Ufish, and percentage of low velocity area, the total number of culvert barrel cells Ncell required to fulfil Equation (1) for Q < Q1 is calculated.

When Ncell < (Ncell)des, the initial design would be capable to provide upstream fish passage at less-than- design flows (Q < Q1). In the negative, i.e. Ncell > (Ncell)des, the revised design must include a larger number of barrel cells. In this case, the afflux for the design discharge would be smaller than the maximum acceptable afflux, and the reduction in upstream flooding might contribute to a lesser total cost of the structure: e.g., with a lower embankment and reduced impact on upstream catchment. The savings might contribute to offset partially the increased cost caused by the larger number of culvert barrel cells.

A detailed design application is presented in the digital appendix (i.e. supplementary material). For both culverts 1 and 2, the step-by-step iterative design procedure is developed for a fish-friendly standard box culvert. Depending upon the characteristic swimming speed of the targeted fish species and guild, the current

9 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

hydraulic engineering design guidelines of box culverts may or not provide an adequate number of barrel cells to achieve upstream fish passage at 10% of the design discharge.

More generally, the calculated results showed two "unexpected" trends (i.e. findings usually not discussed in traditional culvert design guidelines) in terms of the maximum acceptable afflux and tailwater rating curve.

An increase in maximum acceptable afflux hmax yields an increase in upstream specific energy, hence an increased bulk velocity in the barrel, at design discharge Qdes and a narrower barrel. In turn the requirements for upstream fish passage, i.e. Equation (1), are less likely to be met at less-than-design flow: i.e. in particular at Q = Q1 < Qdes, and a large number of cells may be required: Ncell > (Ncell)des. The tailwater rating curve is the relationship between tailwater depth and discharge, or variations of natural downstream water level with water discharges. With outlet control operation at less than design discharges, a larger tailwater depth implies a slower fluid flow in the entire culvert barrel, and Equation (1) is more likely to be fulfilled. While these trends may be physically derived from basic hydrodynamic considerations, they are rarely discussed in current engineering design manuals of culverts, because less-than-design water discharges are not specifically considered.

4.2 Linking fluid dynamics and biology

Intrinsically, open channel fluid dynamics is characterised by the complicated interactions between the water and a number of mechanisms including the boundary friction, gravity and turbulence. Traditionally, these open channel flows have been modelled based upon one-dimensional depth-averaged equations, which predict the mean flow properties, i.e. the bulk velocity Vmean and water depth d, and often encompass a fair level of empiricism: "this simple 1D approach is clearly problematic" (MORVAN et al. 2008, p. 192). By far a most pertinent flow property is the velocity distribution, especially in the vicinity of solid boundaries, because small fish predominantly swim upstream next to the corners and walls (GARDNER 2006, BLANK

2008, JENSEN 2014, KATOPODIS and GERVAIS 2016, WANG et al. 2016a, CABONCE et al. 2019). A complete characterisation of the velocity field requires a detailed investigation which may be undertaken physically in laboratory and numerically using computational fluid dynamics (CFD), possibly theoretically for a few rare simplistic situations. Laboratory measurements must be based upon a large number of data points to characterise the main stream, boundary regions (i.e. next to bed and walls), and secondary flows.

10 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

For example, WANG et al. (2018) and CABONCE et al. (2018,2019) recorded 250-300 sampling points per cross-section for a given flow rate. In aeronautics and industrial flows, the implementation of complex three- dimensional (3D) CFD models has become more commonly used (ROACHE 1998, RIZZI and VOS 1998).

This transition is more recent in open channel flows, with inherent difficulties in applying 3D CFD to free- surface flows, e.g. the air-water interface, complicated geometry and roughness definition (RODI et al. 2013,

KHODIER and TULLIS 2018, ZHANG and CHANSON 2018).

A sound linkage between biology and hydrodynamics is a fundamental requirement to advance our understanding of fish-friendly culvert design based upon physically-sound fish performance and hydrodynamic principles. Despite the recent advances in hydrodynamics of culverts, there remains a gap between our knowledge of the characterisation of turbulence and our understanding of its role on biotic communities. Leading scholars stressed the challenge, specifically the need for "a better understanding of the relationship between the turbulent properties and [their] influence on individual organisms and ecological communities" [...] "to effectively integrate hydraulically realistic information with ecological data" (MADDOCK et al. 2013, p. 432). Several researchers have pointed to the absence of standardised fish swimming tests and data interpretation relevant to engineering design (KEMP 2012, KATOPODIS and

GERVAIS 2016), because of "inconsistent metrics in the published literature" (KEMP 2012, p. 404). Yet there is a physically-based relationship between the local longitudinal velocity and the (mechanical) power and energy required by fish to swim upstream against the discharge (WANG and CHANSON 2018). Thus biology and hydrodynamics are linked and Equation (1) provides the means to deliver a sizeable turbulent low velocity zone (LVZ), as sketched in Figure 6, in line with detailed physical and numerical experiments.

It is however an open question as to what extent the details not considered by the current work will affect fish passage predictions. It is believed that the interactions between fish and hydrodynamics must be appraised within the context and time scales of a small fish traversing a culvert barrel in the upstream direction against the current. A key question is: what does the characteristic swimming speed Ufish relate to?

In a 12 m long 0.5 m wide smooth culvert barrel flume, corresponding to a full-scale barrel cell of a 2-lane road embankment, two fish species, juvenile silver perch (Bidyanus bidyanus) and adult Duboulay's rainbowfish (Melanotaenia duboulayi), were tested in terms of their upstream swimming (WANG et al.

2016a, CABONCE et al. 2017,2018,2019). For both fish species, visual observations and high-speed video

11 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

movies showed that the fish trajectories consisted of a succession of swimming sequences with (a) quasi- stationary motion where fish speed fluctuations were small, (b) short upstream motion facilitated by a few strong tail-beats, and (c) rare burst swimming. The most common observation of upstream fish swimming was the first one: i.e., quasi-stationary motion facing the current. Altogether, the fish took from about one minute to more than 20 minutes, to swim the entire culvert barrel flume, spending about 90% of their time in the bottom corners and along the sidewalls. Based upon such detailed fish kinematic observations, the characteristic swimming speed Ufish should combine the fish swimming endurance performances and their ability to negotiate low-velocity zones.

5. SUMMARY AND CONCLUSION

New guidelines for fish-friendly multi-cell box culvert designs are being developed in NSW (Australia), based upon simple practical and physically-based concepts: (a) the culvert design is optimised for fish passage for Q < Q1, and for flood capacity for Q1 < Q < Qdes, and (b) low-velocity zones in the culvert barrel are defined in terms of a percentage of the wetted flow area where 0 < Vx < Ufish, with Vx the local longitudinal velocity component and Ufish a characteristic fish speed linked to swimming performances of targeted fish species. This study delivers simple guidelines for multi-cell box culvert structures with identical

(or nearly-identical) smooth barrel cells, in line with current engineering practices. Low velocity zones

(LVZs) are provided along the wetted perimeter and next to the culvert barrel corners, where small-bodied fish swim and can minimise their energy expenditure. This approach is novel and relies upon an accurate physically-based knowledge of the entire velocity field in the barrel, specifically the longitudinal velocity map, because fish tend to target LVZ boundaries. It is well-suited to weak-swimming fish, like small-bodied

Australian native fish species, although the method may be applied to a wider range of fish species.

The influence of the relative threshold Q1/Qdes, characteristic fish swimming speed Ufish, and percentage of flow area on the size of box culvert structures was assessed. For smooth culvert barrel invert at natural ground level, the increase in culvert size and cost might become very significant for Ufish < 0.3 m/s and

Q1/Qdes > 0.3, when providing 15% flow area with 0 < Vx < Ufish, with smooth culvert barrel. The increase in culvert size would correspond to a lower bound of the increase in culvert construction costs to achieve fish

12 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

passage compared to a traditional engineering design approach. When the characteristic swimming speed of the targeted fish species is less than 0.3 m/s (Ufish < 0.3 m/s), a different design approach might be required.

One option could target a lower relative threshold Q1/Qdes. Another option could involve a design incorporating a barrel cell with larger low-velocity zones. This could be achieved with boundary roughening and addition of apertures, e.g. baffles, although negative velocities and strong recirculation must be avoided for small-bodied fish, and juveniles of large-bodied fish, since a recent study demonstrated their adverse effects (CABONCE et al. 2018). Further detailed CFD calculations for recessed cell(s) with a lower invert indicate similar trends as those for a culvert barrel invert at natural ground level in terms of cost increase.

The results however showed a significantly more complicated hydrodynamic field in the barrel, in addition to the increased construction costs.

The present study delivers a physically-based rationale for fish-friendly standard box culvert design, embedding state-of-the-art hydrodynamic calculations into current hydraulic engineering design methods to yield cost-effective outcomes. By bridging the gap between engineering and hydrodynamics, such a novel approach may contribute to the restoration of catchment connectivity. The method is more general than previous attempts, yet simple and cost effective enough to be widely endorsed by the various stakeholders.

Finally it is acknowledged that the design approach is focused in culvert barrel design. Complete design guidelines must further include inlet and outlet design recommendations.

6. ACKNOWLEDGMENTS

The authors thank Professor Colin J. APELT (The University of Queensland, Australia), Dr Gangfu ZHANG

(WSP Brisbane, Australia), and Professor Daniel BUNG (FH Aachen University of Applied Science,

Germany) for valuable comments. Further comments from discussions with a number of professional engineers and biologists were considered.

The financial support of Australian Research Council (Grant LP140100225) is acknowledged.

13 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

7. DIGITAL APPENDIX. SAMPLE CALCULATION FOR DESIGN APPLICATION (SUPPLEMENTARY MATERIAL)

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20 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

FIGURE CAPTIONS

Fig. 1 - Standard box culvert structure

(A) Definition sketch of a multi-cell box culvert with invert placed on natural ground level

(B) Multi-cell box culvert structure on Stable Swamp Creek, Salisbury QLD (Australia)

Fig. 2 - Characteristics of the Gara River at Willow Glen north-eastern New South Wales (Data courtesy of

NSW DPI Office of Water) - Catchment area: 121 km2, site 20635

(A) Hydrograph of the Gara River from 15 March 2008 to 15 March 2018

(B) Channel cross-section on 4 Feb. 1997

Fig. 3 - Relative increase in number of cells Ncell/(Ncell)des for fish-friendly multi-cell box culverts as a function of the threshold discharge Q1/Qdes and characteristic fish swimming speed Ufish, with 15% of flow area where 0 < Vx < Ufish

(A) Culvert 1

(B) Culvert 2

Fig. 4 - Relative increase in number of cells Ncell/(Ncell)des for fish-friendly multi-cell box culverts as a function of the percentage of LVZ flow areaa where 0 < Vx < Ufish and characteristic fish swimming speed

Ufish, for a threshold discharge Q1/Qdes = 0.20

(A) Culvert 1

(B) Culvert 2

Fig. 5 - Hydrodynamics of a culvert barrel with recessed invert - Barrel invert elevation 0.3 m below natural ground level

(A) Definition sketch of pooled (recessed) culvert barrel (Culvert 1b)

(B) Longitudinal velocity contours in the culvert barrel (Culvert 1b) for q/qdes = 10% - Black line indicate the free-surface - Flow direction from top right to bottom left, Barrel water depth: 0.83 m, Vmean = 0.22 m/s

21 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

Fig. 6 - Sketch of low velocity zones as defined by Equation (1) in a box culvert barrel, looking downstream

22 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

Fig. 1 - Standard box culvert structure

(A) Definition sketch of a multi-cell box culvert with invert placed on natural ground level

(B) Multi-cell box culvert structure on Stable Swamp Creek, Salisbury QLD (Australia)

23 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

Fig. 2 - Characteristics of the Gara River at Willow Glen north-eastern New South Wales (Data courtesy of

NSW DPI Office of Water) - Catchment area: 121 km2, site 20635

(A) Hydrograph of the Gara River from 15 March 2008 to 15 March 2018

90 80 70 60

/s) 50 3 40 Q (m 30 20 10 0 0 500 1000 1500 2000 2500 3000 3500 4000 Number of days since 15/3/2008 (00:00) (B) Channel cross-section on 4 Feb. 1997 (C) Relationship between water depth and discharge

24 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

1.8

1.6 2.5 1.4

2 1.2

1 1.5 0.8

1 Waterdepth d (m) 0.6 Elevation (m) 0.4 0.5 0.2

0 0 25 35 45 55 65 75 85 0 10 20 30 40 50 60 70 80 90 Distance from left bank (m) Water discharge Q (m3/s)

25 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

(A) Culvert 1

Increase in number of barrel cells 0 25% 50% 75% 100% 125% 150% 175% 200% 225% 250% 0.7 15% Flow Area with 0 < Vx < Ufish 0.6 Q1/Qdes = 10% Q1/Qdes = 20% Q1/Qdes = 30% 0.5 Q1/Qdes = 50%

0.4 (m/s)

fish 0.3 U

0.2

0.1

0 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 N /(N ) cell cell des (B) Culvert 2

Increase in number of barrel cells 0 25% 50% 75% 100% 125% 150% 175% 200% 225% 250% 0.7 15% Flow Area with 0 < Vx < Ufish 0.6 Q1/Qdes = 50% Q1/Qdes = 30% Q1/Qdes = 20% 0.5 Q1/Qdes = 10%

0.4 (m/s)

fish 0.3 U

0.2

0.1

0 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 N /(N ) cell cell des

26 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

Ufish, for a threshold discharge Q1/Qdes = 0.20

(A) Culvert 1

Increase in number of barrel cells 0 25% 50% 75% 100% 125% 150% 175% 200% 225% 250% 0.6 Q1/Qdes = 0.2 - 0 < Vx < Ufish for 20% flow area 0.5 15% flow area 10% flow area 0.4

(m/s) 0.3 fish U 0.2

0.1

0 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 N /(N ) cell cell des (B) Culvert 2

Increase in number of barrel cells 0 25% 50% 75% 100% 125% 150% 175% 200% 225% 250% 0.6 Q1/Qdes = 0.2 - 0 < Vx < Ufish for 20% flow area 0.5 15% flow area 10% flow area 0.4

(m/s) 0.3 fish U 0.2

0.1

0 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 N /(N ) cell cell des

27 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

28 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

Fig. 5 - Hydrodynamics of a culvert barrel with recessed invert - Barrel invert elevation 0.3 m below natural ground level

(A) Definition sketch of pooled (recessed) culvert barrel (Culvert 1b)

29 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

Fig. 6 - Sketch of low velocity zones as defined by Equation (1) in a box culvert barrel, looking downstream

30 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364- 152X).

Table 1 - Design guidelines for freshwater fish passage in standard culverts

Reference Country & Targeted fish species Design criteria Flow conditions Region FAIRFULL and Australia Depth > 0.2-0.3 m Smooth culvert WHITERIDGE Vmean < 0.3 m/s for d < 0. 5 m (2003) BATES et al. USA, Trout, pink salmon, chum salmon, Depth > 0.24 to 0.30 m Smooth culvert (2003) Washington chinook, coho, sockeye, steelhead Vmean < 0.61 to 1.83 m/s CAHOON et al. USA, Montana Yellowstone cutthroat trout Vmean < 1.9-2.7 m/s Box culvert geometry (2007) (Oncorhynchus clarkii bouvieri), rainbow trout (Oncorhynchus mykiss) KILGORE et al. USA Minimum water depth for Qmin < Qhigh < Qdes (2010), SCHALL Q > Qmin et al. (2012) Maximum bulk velocity for Q < Qhigh COURRET (2014) France Trout, European bullhead (Cottus Baffles, macro-roughness From drought to 2-3 gobio), brook lamprey (Lampetra times the mean annual planeri), spined loach (Cobitis discharge taenia), common minnow (Phoxinus phoxinus), eel, crayfish DWA (2014) Germany European species Vmean < Ufish Q330 < Q < Q30 each year incl. barbel, brown trout, eel, Depth > 2.5Fish height grayling, salmon, ... Baffles/crossbars, macro- roughness

Notes: Q: water discharge; Q30: flow rate occurring no more than 30 days per year; Q330: flow rate occurring no more than 330 days per year; q: unit discharge; So: bed slope; Vmean: bulk velocity; z: vertical elevation above the invert.

31 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364- 152X).

Table 2 - Observations and derived recommendations for freshwater fish passage in standard culverts

Reference Country & Targeted fish species Design criteria Flow conditions Type of study Region CHORDA et al. France Baffles So = 0.01 to 0.05 Laboratory work. (1995) GARDNER (2006) USA, North Bluehead chub (Nocomis Vmean < 0.55 m/s Smooth culvert Laboratory work. Carolina leptocephalus), redbreast Sunfish Box culvert geometry. (Lepomis auritus), Johnny Darter (Etheostoma nigrum), bluegill (Lepomis macrochirus), margined madtom (Noturus insignis), swallowtail shiner (Notropisprocne) 3 BLANK (2008) USA, Montana Yellowstone cutthroat trout Vx(z = 0.06 m) < 1 to 2 m/s Base flow: 0.28 m /s Field observations. 2 (Oncorhynchus clarkii bouvieri) q < 0.4 to 0.57 m /s So = 0.02 to 0.05 Box culvert geometry. MONK and USA, Utah Leatherside chub (Lepidomeda Vx(z = 0.02 m) < Ufish Lbarrel ~ 20 m Field observations. HOTCHKISS aliciae), speckled dace (Rhinichthys 0.5 < Q < 1.6 m3/s Box culvert geometry. (2012) osculus) 0.073 < q < 0.24 m2/s

Notes: d: water depth; Lbarrel: barrel length; Q: water discharge; So: bed slope; Vmean: bulk velocity; Vx: local longitudinal velocity; z: vertical elevation above the invert.

32 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

Table 3 - Characteristics of multi-cell box culvert structures

Culvert 1 Culvert 1b Culvert 2 Hydrology Gara River NSW Gara River NSW Tailwater conditions Gauge data Gauge data Uniform equilibrium flow So 0 0 0.0012 Design event 1-in-1 year event 1-in-1 year event (2008-2018) (2008-2018) 3 Qdes (m /s) 20.0 -- 4.8 Qdes (ML/day) 1,728 -- 415 2 qdes (m /s) 2.20 1.92 0.78 (dtw)des (m) 0.976 0.976 0.457 Lbarrel (m) 8 8 14 Dcell (m) 1.0 1.3 0.5 Bcell (m) 1.3 1.0 1.0 Boundary roughness smooth concrete smooth concrete smooth concrete Barrel invert natural ground level 0.3 m below natural natural ground level ground level Maximum acceptable afflux 0.55 0.55 0.20 hmax (m) 1 1 Number of cells (Ncell)des 7 () 1 7 ( ) (Vmean)des (m/s) 1.74 1.9 2.0

Notes: Bcell: internal barrel cell width (Fig. 1a), Dcell: internal barrel cell height; (dtw)des: tailwater depth at

1 design flow; Lbarrel: culvert barrel length; So: bed slope; Vmean: bulk velocity in the barrel; ( ) Minimum cross- section area for inlet control operation at design flow conditions.

33 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish - Supplementary Material

by Xinqian LENG, Hubert CHANSON, Matthews GORDOS and Marcus RICHES

Sample Calculation for Design Application

A.1 Presentation

This appendix aims to demonstrate design application examples of the proposed fish-friendly culvert design guidelines. Detailed procedure for designing a fish-friendly culvert is shown herein using two sample cases, being Culvert 1 and 2 (Table 3). The procedure can be summarised into 2 stages: (1) finding the optimum design to pass design flow discharge Qdes for a standard box culvert and (2) finding the number of additional culvert cells required to pass fish at less-than-design flow discharge i.e. 10% of the design flow (0.1Qdes).

Note that the proposed design guidelines focused primarily on the design of the culvert barrel, using standard box culverts, assuming construction on a mild slope. Designs of culverts outside this scope will not be detailed in the current application.

Both stages of calculations are iterative processes. To find the optimum design for Qdes with a maximum acceptable afflux hmax, the minimum number of boxes required to achieve inlet control is calculated. Two alternative methods may be used, being an engineering design nomograph (Concrete Pipe Association of

Australasia 2012) or a set of theoretical equations based on critical conditions and conservation of energy

(HENDERSON 1966, CHANSON 2004, CHANSON and LENG 2018). The theoretical equations give the design discharge per unit width:

Qdes 22 1.5 CgHz (H1-zinlet) ≤ 1.2Dcell (A.1) B33D1inlet

Qdes CD  2g  H  z  CD (H1-zinlet) > 1.2Dcell (A.2) B cell 1 inlet cell

where B is the internal barrel width and Dcell is the internal barrel height, (H1-zinlet) is equivalent of the head water level (H1-zinlet = dtw + afflux). When the headwater is less than 1.2 times the cell height, a free-surface inlet is observed and Equation A.1 should be used. Otherwise a submerged entrance and free-surface barrel

A-1 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

flow occur, and Equation A.2 is to be used. The constants CD and C correspond to the shape of the inlet. For the most common square-edged inlet, CD = 0.9 and C = 0.6.

Next, the design must be checked against outlet control situation, using the outlet control nomograph

(Concrete Pipe Association of Australasia 2012). The nomograph will give the afflux for the calculated number of cells at outlet control. Ultimately, whichever afflux is bigger controls the flow, e.g. if afflux for inlet control > afflux for outlet control, inlet control is achieved; otherwise, the number of cells must be increased and outlet control calculations are repeated until the afflux is less than hmax.

Once the number of cells (Ncell)des are obtained at design flow conditions, numerical CFD modelling is performed for a single cell to examine the complete velocity field throughout the culvert cell. Using contour plots of longitudinal velocity at different cross-sections of the culvert barrel, the flow area under certain velocity magnitudes can be derived. In section 2, we consider that at least 15% of the flow area is under characteristic fish swimming speed Ufish, with the range of Ufish being 0.2 - 0.5 m/s. Another criterion might include a minimum area of low velocity zone at the barrel bottom corners to pass the fish bodies. If the results of numerical models do not satisfy the required criteria of fish-friendly design, the number of cells must be revised by adding a further cell, and the modelling is to be repeated with an updated cell number configuration.

Figure A-1 summarises the iterative design procedure for a fish-friendly standard box culvert.

A-2 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

Fig. A-1 - Flow chart for steps to achieve optimum design at design flow conditions

A.2 Sample case 1: Culvert 1

The design flow conditions for sample case 1 (Culvert 1) is detailed in Table 3. The design flow is a 1 in 1

3 year event with design discharge Qdes = 20 m /s (1728 ML/day). The length of the road embankment, i.e. length of the culvert barrel, is Lbarrel = 8 m. The cells are rectangular smooth-concrete boxes of the same size: width Bcell = 1.3 m and height Dcell = 1 m. The culvert barrel sat on a horizontal flat flood plain (zero slope).

Maximum acceptable afflux of the site is hmax = 0.55 m. The tailwater rating curve is extracted from existing gauge data, for which the tailwater depth dtw is fitted as: 0.28415 dtw  0.416536 Q (A.3)

At design flow conditions, the tailwater depth is dtw = 0.976 m.

Using both engineering nomographs and theoretical equations (HENDERSON 1966, CHANSON 2004), the calculation yields a required number of cells (Ncell)des = 7. The afflux for a seven-cell structure was approximately 0.362 m at design flow rate.

Numerical CFD modelling was conducted for less-than-design flow condition at 10% of the design discharge

3 TM (0.1Qdes = 2 m /s). The flow was modelled by ANSYS Fluent v. 18.0. The model used a standard k-ɛ method to resolve the turbulence, and used a Volume of Fluid (VOF) method to resolve the two-phase air- water interface. The k- turbulence model is a simple model well-suited to smooth boundaries, including in open channels (OBERKAMPF et al. 2004, RODI 2017). It was selected in the current study for reduced computational times. More complicated turbulence models should indeed be considered for more complicated boundary treatments (e.g. ZHANG and CHANSON 2018). In the current study, transient flow simulation was used for all numerical test cases, where an initial simulation was performed using a coarse mesh, and the results were further interpolated on a refined mesh for transient simulation until convergence

(LENG and CHANSON 2018). The transient formulation was solved implicitly with a second order upwind scheme for momentum, first order upwind scheme for turbulent kinetic energy and turbulent dissipation rate.

The convergence was ensured by reducing residuals of all parameters to 10-4 or less. All simulations were run for a physical time span of over 90 s to ensure a steady equilibrium flow and the conservation of mass was achieved between inlet and outlet. Figure A-2 shows the modelled results of the longitudinal velocity

A-3 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

contour near the downstream end of the culvert barrel (0.5 m upstream from the barrel exit). The percentage of flow area under certain velocity magnitudes is shown in Figure A-3.

When the characteristic fish swimming speed Ufish is set to 0.5 m/s, the results showed that the current design

(seven-cell structure) would satisfy the fish passage requirements. The diagonal length of the low velocity zone (Ufish < 0.5 m/s) also fulfil a minimum requirement for 25 mm × 25 mm corner area. If the characteristic fish swimming speed is set to Ufish = 0.4 m/s or below, the current design would fail to satisfy the minimum

15% of flow area and a larger number of cells would be required.

Fig. A-2 - Longitudinal velocity contour of a single cell in a seven-cell structure of case 1 (Culvert 1) at 10%

3 of design flow (0.1Qdes = 2 m /s); results near the downstream end of the culvert barrel (0.5 m upstream from the barrel exit); free-surface denoted by solid black line; diagonal length of low velocity zone denoted by black dashed line

A-4 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

90 85 Culvert 1 80 75

(%) 70 x 65 60 55 50 45 40 35 30 25 20

Fraction of area less than V of Fraction 15 10 5 0 0.18 0.24 0.3 0.36 0.42 0.48 Vx (m/s) Fig. A-3 - Percentage of flow area under certain velocity values for a single cell in a seven-cell structure of

3 case 1 (Culvert 1) at 10% of design flow (0.1Qdes = 2 m /s); results near the downstream end of the culvert barrel (0.5 m upstream from the barrel exit)

A.3 Sample case 2: Culvert 2

The design flow conditions for sample case 2 (Culvert 2) are presented in Table 3. The design flow is Qdes =

3 4.8 m /s (415 ML/day). The length of the culvert barrel is Lbarrel = 14 m, and the cells are identical rectangular smooth-concrete boxes: width Bcell = 1 m and height Dcell = 0.5 m. The slope of the flood plain is

0.0012 and the maximum acceptable afflux at design flow is hmax = 0.2 m. The tailwater depth dtw is assumed to be at uniform equilibrium, and the tailwater rating curve is best fitted as: 0.598698 dtw  0.178688 Q (A.4)

with the tailwater depth at design flow condition: dtw = 0.457 m.

Using both engineering nomographs and theoretical equations (HENDERSON 1966, CHANSON 2004), the calculation yields a required number of cells: (Ncell)des = 7. The afflux for a seven-cell culvert structure is approximately 0.168 m.

Numerical CFD modelling was conducted for less-than-design flow condition at 10% of the design discharge

3 (0.1Qdes = 0.48 m /s). Figure A-4 shows the modelled results of the longitudinal velocity contour near the downstream end of the culvert barrel, i.e. 2 m upstream of the barrel exit. The percentage of flow area under

A-5 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

specific velocity magnitudes is shown in Figure A-5. If the characteristic fish swimming speed Ufish is set to

0.5 m/s, the current design (seven-cell structure) would satisfy the fish passage requirements for minimum area (15% of the flow area).

Discussion

While the present structure may fulfil the requirement for upstream passage (Eq. (1)), the low velocity zones are shallow and thin. In the barrel corner, the diagonal length of the low velocity zone (LVZ) is shown in

Figure A-4. For Q = 0.1Qdes and Ufish < 0.5 m/s, the corner LVZ would be less than 20 m thick, which might not suitable for a number of fish species. In such a case, a different and more elaborate design might be required. This could include a recessed barrel invert, a downstream pool wall to induce some backwater effect, or the installation of baffles, all of which would increase the water depth the barrel and hence the size of the LVZ.

Fig. A-4 - Longitudinal velocity contour of a single cell in a six-cell structure of case 2 (Culvert 2) at 10% of

3 design flow (0.1Qdes = 0.48 m /s); results near the downstream end of the culvert barrel (2 m upstream from the barrel exit); free-surface denoted by solid black line; diagonal length of low velocity zone denoted by black dashed line

A-6 LENG, X., CHANSON, H., GORDOS, M., and RICHES, M. (2019). "Developing Cost-Effective Design Guidelines for Fish-Friendly Box Culverts, with a Focus on Small Fish." Environmental Management, Vol. 63, No. 6, pp. 747-758 & Supplementary material (7 pages) (DOI: 10.1007/s00267-019-01167-6) (ISSN 0364-152X).

100 Culvert 2 90 80 (%) x 70 60 50 40 30 20 Fraction of area less than V than less area of Fraction 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Vx (m/s) Fig. A-5 - Percentage of flow area under certain velocity values for a single cell in a six-cell structure of case

3 2 (Culvert 2) at 10% of design flow (0.1Qdes = 0.48 m /s); results near the downstream end of the culvert barrel (2 m upstream from the barrel exit)

A-7